Question

Notify Me Bookmark

The graph of y = f(x) is given. Match each equation with its graph and give reasons for your choices. (a) y = f(x − 4) (b) y = f(x) + 3 (c) y = 1 3 f(x) (d) y = −f(x + 4) (e) y = 2f(x + 6)

The graph of y = f(x) is given. Match each equation with its graph and give reasons for your choices. (a) y = f(x − 4) (b) y = f(x) + 3 (c) y = 1 3 f(x) (d) y = −f(x + 4) (e) y = 2f(x + 6)

Image text
  1. The graph of y = f ( x ) is given. Match each equation with its graph and give reasons for your choices. (a) y = f ( x − 4 ) (b) y = f ( x ) + 3 (c) y = 1 3 f ( x ) (d) y = − f ( x + 4 ) (e) y = 2 f ( x + 6 )

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

Explain how each graph is obtained from the graph of y = f(x). (a) y = f(x)+6 Stretch the graph horizontally and vertically by a factor of 6 . Shift the graph 6 units to the right. Shift the graph 6 units upward. Shift the graph 6 units downward. Shift the graph 6 units to the left. (b) y = f(x+6) Shift the graph 6 units to the right. Shift the graph 6 units upward. Stretch the graph horizontally and vertically by a factor of 6 . Shift the graph 6 units downward. Shift the graph 6 units to the left. (c) y = 6f(x) Shift the graph 6 units upward. Shrink the graph horizontally by a factor of 6 . Stretch the graph horizontally and vertically by a factor of 6 . Stretch the graph vertically by a factor of 6 . Shift the graph 6 units to the left. (d) y = f(6x) Shift the graph 6 units upward. Shift the graph 6 units to the left. Stretch the graph vertically by a factor of 6 . Stretch the graph horizontally and vertically by a factor of 6 . Shrink the graph horizontally by a factor of 6 . (e) y = −f(x)−1 First reflect the graph about the y-axis, and then shift it 1 unit downward. First reflect the graph about the y-axis, and then shift it 1 unit upward. First reflect the graph about the x-axis, and then shift it 1 unit downward. First reflect the graph about the x-axis, and then shift it 1 unit upward. First reflect the graph about the x-axis, and then shift it 1 unit left. (f) y = 6f(16 x) Shrink the graph horizontally by a factor of 6. Stretch the graph horizontally and vertically by a factor of 6 . Stretch the graph vertically by a factor of 6 . Shrink the graph horizontally and vertically by a factor of 6. Stretch the graph horizontally by a factor of 6.Explain how each graph is obtained from the graph of y = f(x). (a) y = f(x)+6 Stretch the graph horizontally and vertically by a factor of 6 . Shift the graph 6 units to the right. Shift the graph 6 units upward. Shift the graph 6 units downward. Shift the graph 6 units to the left. (b) y = f(x+6) Shift the graph 6 units to the right. Shift the graph 6 units upward. Stretch the graph horizontally and vertically by a factor of 6 . Shift the graph 6 units downward. Shift the graph 6 units to the left. (c) y = 6f(x) Shift the graph 6 units upward. Shrink the graph horizontally by a factor of 6 . Stretch the graph horizontally and vertically by a factor of 6 . Stretch the graph vertically by a factor of 6 . Shift the graph 6 units to the left. (d) y = f(6x) Shift the graph 6 units upward. Shift the graph 6 units to the left. Stretch the graph vertically by a factor of 6 . Stretch the graph horizontally and vertically by a factor of 6 . Shrink the graph horizontally by a factor of 6 . (e) y = −f(x)−1 First reflect the graph about the y-axis, and then shift it 1 unit downward. First reflect the graph about the y-axis, and then shift it 1 unit upward. First reflect the graph about the x-axis, and then shift it 1 unit downward. First reflect the graph about the x-axis, and then shift it 1 unit upward. First reflect the graph about the x-axis, and then shift it 1 unit left. (f) y = 6f(16 x) Shrink the graph horizontally by a factor of 6. Stretch the graph horizontally and vertically by a factor of 6 . Stretch the graph vertically by a factor of 6 . Shrink the graph horizontally and vertically by a factor of 6. Stretch the graph horizontally by a factor of 6.
Solution
0 0

Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of f as follows. (a) Shift 2 units upward. y = f(x−2) y = 2f(x) y = f(x)+2 y = 1 2 − f(x) y = f(x)−2 (b) Shift 2 units downward. y = 1 2 − f(x) y = f(x−2) y = f(x)+2 y = 2 f(x) y = f(x)−2 (c) Shift 2 units to the right. y = f(x−2) y = 2 f(x) y = 1−f(x) y = f(x)+2 y = f(x)−2 (d) Shift 2 units to the left. y = f(x−2) y = f(x+2) y = f(x)−2 y = 1 2 − f(x) y = f(x)+2 (e) Reflect about the x-axis. y = f(x)+2 y = f(x−2) y = 1 2 −f(x) y = −f(x) y = 2f(x) (f) Reflect about the y-axis. y = f(x−2) y = 1 2 −f(x) y = f(x)+2 y = 2f(x) y = f(−x) (g) Stretch vertically by a factor of 2 . y = 1 2 −f(x) y = 2f(x) y = f(x)+2 y = f(x−2) y = f(x)−2 (h) Shrink vertically by a factor of 2 . y = f(x)−2 y = f(x)+2 y = f(x−2) y = 2 f(x) y = 12−f(x)Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of f as follows. (a) Shift 2 units upward. y = f(x−2) y = 2f(x) y = f(x)+2 y = 1 2 − f(x) y = f(x)−2 (b) Shift 2 units downward. y = 1 2 − f(x) y = f(x−2) y = f(x)+2 y = 2 f(x) y = f(x)−2 (c) Shift 2 units to the right. y = f(x−2) y = 2 f(x) y = 1−f(x) y = f(x)+2 y = f(x)−2 (d) Shift 2 units to the left. y = f(x−2) y = f(x+2) y = f(x)−2 y = 1 2 − f(x) y = f(x)+2 (e) Reflect about the x-axis. y = f(x)+2 y = f(x−2) y = 1 2 −f(x) y = −f(x) y = 2f(x) (f) Reflect about the y-axis. y = f(x−2) y = 1 2 −f(x) y = f(x)+2 y = 2f(x) y = f(−x) (g) Stretch vertically by a factor of 2 . y = 1 2 −f(x) y = 2f(x) y = f(x)+2 y = f(x−2) y = f(x)−2 (h) Shrink vertically by a factor of 2 . y = f(x)−2 y = f(x)+2 y = f(x−2) y = 2 f(x) y = 12−f(x)Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of f as follows. (a) Shift 2 units upward. y = f(x−2) y = 2f(x) y = f(x)+2 y = 1 2 − f(x) y = f(x)−2 (b) Shift 2 units downward. y = 1 2 − f(x) y = f(x−2) y = f(x)+2 y = 2 f(x) y = f(x)−2 (c) Shift 2 units to the right. y = f(x−2) y = 2 f(x) y = 1−f(x) y = f(x)+2 y = f(x)−2 (d) Shift 2 units to the left. y = f(x−2) y = f(x+2) y = f(x)−2 y = 1 2 − f(x) y = f(x)+2 (e) Reflect about the x-axis. y = f(x)+2 y = f(x−2) y = 1 2 −f(x) y = −f(x) y = 2f(x) (f) Reflect about the y-axis. y = f(x−2) y = 1 2 −f(x) y = f(x)+2 y = 2f(x) y = f(−x) (g) Stretch vertically by a factor of 2 . y = 1 2 −f(x) y = 2f(x) y = f(x)+2 y = f(x−2) y = f(x)−2 (h) Shrink vertically by a factor of 2 . y = f(x)−2 y = f(x)+2 y = f(x−2) y = 2 f(x) y = 12−f(x)
Solution
0 0

Match each equation with its graph. Explain your choices. (Don't use a computer or graphing calculator. ) (a) y = 5x f F g G (b) y = 5 x f G g F (c) y = x5 G f F g (d) y = x5 F G g f
Solution
0 0